I've created a widget based upon the sample code and using https://user:pass@website works fine in the simulator, but always gives an error -401 on the watch. I am using an Android phone.
According to the docs an error of -401 is "INVALID_HTTP_HEADER_FIELDS_IN_NETWORK_RESPONSE" which seems to indicate something is being returned that wasn't expected and/or supported. Can you share more details about the request you are sending? Or at the very least share the details of what the response is sending back?